Bar width depends on what type of bar: risers are the widest, followed by flat, and drop bars are the narrowest. Only drop bars are directly shoulder width + 2 cms. The rest are much wider, especially if you run a modern setup with shorter stem and riser bars.

For example, my shoulder width is about 32cms (less than 13") but my riser is 23.5" and flat bar is 23".

Modern setups are already using 700mm to 800mm wide bars. If your shoulders are really 23" wide, you should really look at a wider setup